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Jee Main 2025 — Medium JEE math MCQ

If the domain of the function \( \log_5 (18x - x^2 - 77) \) is \( (\alpha, \beta) \) and the domain of the function \( \log(x-1) \left( \frac{2x^2 + 3x - 2}{x^2 - 3x - 4} \right) \) is \( (\gamma, \delta) \), then \( \alpha^2 + \beta^2 + \gamma^2 \) is equal to
  1. A. 195
  2. B. 179
  3. C. 186
  4. D. 174

Solution

The correct option is **C**. (C. 186)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If the domain of the function log⁡5(18x−x2−77) \log_5 (18x - x^2 - 77) is (α,β) (\alpha, \beta) and the domain of the function log⁡(x−1)(2x2+3x−2x2−3x−4) \log(x-1) \left( \frac{2x^2 + 3x - 2}{x^2 - 3x - 4} \right) is (γ,δ) (\gamma, \delta) , then α2+β2+γ2 \alpha^2 + \beta^2 + \gamma^2 is equal to
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